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Graphs having no quantum symmetry

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Teodor Banica, Julien Bichon, Gaetan Chenevier

Combinatorics · Submitted 10 May 2006

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove that for $p>>k$ the graph has no quantum symmetry, in the sense that the quantum automorphism group reduces to the classical automorphism group.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0605257 (version 2)
Pith IDGHUJGU2Q, Pith's permanent record of this paper and its review
CitationGaetan Chenevier, Julien Bichon, Teodor Banica. "Graphs having no quantum symmetry." arXiv:math/0605257 (2006). https://pith.science/paper/GHUJGU2Q
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,869 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.56 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.52 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We consider circulant graphs having $p$ vertices, with $p$ prime. To any such graph we associate a certain number $k$, that we call type of the graph. We prove that for $p>>k$ the graph has no quantum symmetry, in the sense that the quantum automorphism group reduces to the classical automorphism group.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider circulant graphs having $p$ vertices, with $p$ prime. background 0.67 0.28 0.02 asserted 0.55
s1 To any such graph we associate a certain number $k$, that we call type of the graph. contribution 0.51 0.88 0.02 asserted 0.94
s2 We prove that for $p>>k$ the graph has no quantum symmetry, in the sense that the quantum automorphism group reduces to the classical automorphism group. result 0.99 0.95 0.94 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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sources read
  • arXiv listing abstract v2
not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We consider circulant graphs having $p$ vertices, with $p$ prime. To any such graph we associate a certain number $k$, that we call type of the graph. We prove that for $p>>k$ the graph has no quantum symmetry, in the sense that the quantum automorphism group reduces to the classical automorphism group.

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How the literature uses it

2 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 2 sentences without a confident label

Cites it as background 1 paper
  • The study of quantum permutation groups — quantum variants of the symmetric groups $S_n$ in noncommutative topology — was suggested by Connes, and carried out by Wang, Banica, Bichon and others [ref] .

    A compositional approach to quantum functions · Related work · 1.00

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